A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem

Figure 2

Relationship between distances on solution space and those on Lagrangian space (among locally optimal Lagrangian vectors). ^∗𝑥-axis: distance between Lagrangian vectors, 𝑦-axis: distance between binary solution vectors, and 𝜌: Pearson correlation coefficient.

(a) 5.100: 𝜌=0.91

(b) 5.250: 𝜌=0.96

(c) 5.500: 𝜌=0.97

(d) 10.100: 𝜌=0.80

(e) 10.250: 𝜌=0.92

(f) 10.500: 𝜌=0.96

(g) 30.100: 𝜌=0.60

(h) 30.250: 𝜌=0.80

(i) 30.500: 𝜌=0.91